IZA DP No. 3921
How Much Does Immigration Boost Innovation?
Jennifer HuntMarjolaine Gauthier-Loiselle
DI
SC
US
SI
ON
PA
PE
R S
ER
IE
S
Forschungsinstitutzur Zukunft der ArbeitInstitute for the Studyof Labor
January 2009
How Much Does Immigration Boost
Innovation?
Jennifer Hunt McGill University,
NBER and IZA
Marjolaine Gauthier-Loiselle Princeton University
Discussion Paper No. 3921 January 2009
IZA
P.O. Box 7240 53072 Bonn
Germany
Phone: +49-228-3894-0 Fax: +49-228-3894-180
E-mail: [email protected]
Any opinions expressed here are those of the author(s) and not those of IZA. Research published in this series may include views on policy, but the institute itself takes no institutional policy positions. The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between science, politics and business. IZA is an independent nonprofit organization supported by Deutsche Post World Net. The center is associated with the University of Bonn and offers a stimulating research environment through its international network, workshops and conferences, data service, project support, research visits and doctoral program. IZA engages in (i) original and internationally competitive research in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research results and concepts to the interested public. IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available directly from the author.
IZA Discussion Paper No. 3921 January 2009
ABSTRACT
How Much Does Immigration Boost Innovation?*
We measure the extent to which skilled immigrants increase innovation in the United States by exploring individual patenting behavior as well as state-level determinants of patenting. The 2003 National Survey of College Graduates shows that immigrants patent at double the native rate, and that this is entirely accounted for by their disproportionately holding degrees in science and engineering. These data imply that a one percentage point rise in the share of immigrant college graduates in the population increases patents per capita by 6%. This could be an overestimate of immigration's benefit if immigrant inventors crowd out native inventors, or an underestimate if immigrants have positive spill-overs on inventors. Using a 1940-2000 state panel, we show that immigrants do have positive spill-overs, resulting in an increase in patents per capita of 9-18% in response to a one percentage point increase in immigrant college graduates. We isolate the causal effect by instrumenting the change in the share of skilled immigrants in a state with the state's predicted increase in the share of skilled immigrants. We base the latter on the 1940 distribution across states of immigrants from various source regions and the subsequent national increase in skilled immigrants from these regions. JEL Classification: J61, D24, O32 Keywords: immigration, innovation Corresponding author: Jennifer Hunt Department of Economics University of British Columbia 997-1873 East Mall Vancouver B.C. V6T 1Z1 Canada E-mail: [email protected] * We are grateful to David Munroe for excellent research assistance, and for helpful comments to Francisco Alvarez-Cuadrado, Leah Brooks, David Card, Lee Fleming, Rachel Friedberg, David Green, Francisco Gonzales, Judy Hellerstein, Chad Jones, Bill Kerr, Daniel Parent, Giovanni Peri, Steve Pischke, Regina Riphahn, Eric Stuen and Dee Suttiphisal, seminar participants at the London City University, London School of Economics, NBER (Productivity and Labor Studies), Nürnberg, Simon Fraser, University College London and the SoLE/EALE Transatlantic Conference, and several friends holding patents. We thank Bill Kerr, Nicole Fortin, and Jim Hirabayashi of the USPTO for data and Deven Parmar for obtaining and formatting the USPTO data. Hunt is also affiliated with the CReAM, CEPR, IZA and DIW-Berlin, and acknowledges the Social Science and Humanities Research Council of Canada for financial support.
Economists have studied the impact of immigration on a variety of host country out-
comes. For example, Card (2007) considers U.S. immigration’s impact on population
growth, skill composition, internal migration, wages, rents, taxes and the ethnic and
income composition of neighborhoods and schools. In contrast, the impact of immigra-
tion on innovation has received less attention. In addition to the direct contributions of
immigrants to research, immigration could boost innovation indirectly through positive
spill–overs on fellow researchers, the achievement of critical mass in specialized research
areas, and the provision of complementary skills such as management and entrepreneur-
ship. Some tantalizing facts hint at the possible importance of these effects for the United
States. Compared to a foreign–born population of 12% in 2000, 26% of U.S.–based Nobel
Prize recipients from 1990–2000 were immigrants (Peri 2007), as were 25% of founders of
public venture–backed U.S. companies in 1990–2005 (Anderson and Platzer 2006), and
founders of 25% of new high–tech companies with more than one million dollars in sales
in 2006 (Wadhwa et al. 2007). Immigrants are over–represented among members of the
National Academy of Sciences and the National Academy of Engineering, among authors
of highly–cited science and engineering journal articles, and among founders of bio–tech
companies undergoing IPOs (Stephan and Levin 2001). Kerr (2007) documents the surge
in the share of U.S. patents awarded to U.S.–based inventors with Chinese and Indian
names to 12% of the total by 2004, and Wadhwa et al. (2007) find that non–U.S. citizens
account for 24% of international patent applications from the United States.
The goal of our paper is to assess the impact of skilled immigration on innovation
as measured by U.S. patents per capita. The purpose of studying patents is to gain in-
sight into technological progress, a driver of productivity growth and ultimately economic
growth. If immigrants increase patents per capita, they may increase output per capita
and make natives better off. This is an important consideration for the debate concerning
how many and what type of immigrants should be admitted to the United States, and
particularly for the discussion of the appropriate number of employer–sponsored H–1B
visas for skilled (especially science and engineering) workers. The context of the dis-
cussion is the shift from European to low and middle–income source countries since the
1
Immigration Act of 1965, and the concomitant faster increase in unskilled immigration
than skilled immigration.
One way skilled immigrants could increase patenting per capita is through a greater
concentration than natives in science and engineering occupations. Immigrants are likely
to be over–represented in such occupations, since scientific and engineering knowledge
transfers easily across countries: it does not rely on institutional or cultural knowledge, is
not associated with occupations with strict licensing requirements like medicine, and does
not require the sophisticated language skills of a field like law.1 Skilled immigrants could
also increase patenting per capita if a combination of immigration policies and immigrant
self–selection leads them to be more educated or of higher unobserved inventive ability.
Even immigrants who do not patent themselves may increase patenting by providing
complementary skills to inventors, such as entrepreneurship. Immigrant inventors may in
turn make natives more inventive. Conversely, immigrant inventors’ contributions could
be offset by negative spill–overs, for example, if their presence discourages natives from
working in science and engineering.2
After establishing theoretical propositions concerning the decision of scientists and
engineers to emigrate, we begin our empirical analysis by examining how much immigrants
patent using the 2003 National Survey of College Graduates (NSCG), which contains
information on both patenting activity and birth place. The individual–level data allow
us to gauge the impact of immigrants on patents per capita under the assumption that
immigrants do not influence the behavior of natives or other immigrants, and allow us to
examine whether immigrants patent more than natives because they have higher inventive
ability or merely different education or occupations.
In order to account for immigrants’ possible influence on natives or other immigrants,
we turn to a panel of U.S. states from 1940–2000, based on data from the U.S. Patent
and Trademark Office, the decennial censuses and other sources. We provide estimates
1See Chiswick and Taengnoi (2007) and Peri and Sparber (2008) for evidence.2In the most relevant paper, Borjas (2006) finds that immigrants do not crowd out natives as a whole
from graduate school.
2
of skilled immigrants’ impact on patents per capita that encompass both immigrants’
own patenting and any positive or negative spill–overs immigrants might have. To obtain
the causal effect of immigrants despite their endogenous choice of destination state, we
difference the data across census years, and instrument the change in the share of skilled
immigrants in a state with the state’s predicted increase in the share of skilled immigrants.
We base the latter on the 1940 distribution across states of immigrants from various source
regions and the subsequent national increase in skilled immigrants from these regions.
We contribute to two understudied areas, the impact of immigration on innovation
and the individual determinants of innovation, as well as to the study of the regional
determinants of innovation. Our work is also relevant for the macroeconomic growth
literature, where the link between innovation and the number of researchers is the key to
growth.3
We go beyond the most closely related paper linking immigration and innovation, Peri
(2007), by adding individual–level analysis, extending the state panel, using instrumen-
tal variables to correct for endogeneity, and defining skilled immigration more broadly
and consistently across time. These considerations also distinguish our paper from the
time–series analysis of Chellaraj, Maskus and Mattoo (2008). Both of these papers find
skilled immigration increases U.S. patenting. Our analysis is more general than that of
Stuen, Mobarak and Maskus (2007) and Kerr and Lincoln (2008). The former authors find
that immigrant students increase U.S. university patenting and science and engineering
publishing. The latter authors find that when the national population of H–1B visa–
holders increases, patenting by inventors with Indian and Chinese names rises in states
that have many H–1B applications. A related paper by Niebuhr (2006) concludes that
German regions with more diverse worker nationalities (as measured by the Herfindahl
index) patent more. The result is not robust to region fixed effects, however, no doubt
in part because she has only two years of data close in time (1997 and 1999). Paserman
(2008) finds no effect of skilled immigration on Israeli manufacturing productivity. We
are not aware of previous papers with regression analysis of the individual determinants of
3Aghion and Howitt (1992), Grossman and Helpman (1991a,b), Jones (1995), Romer (1990).
3
patenting, though Morgan, Kruytbosch and Kannankutty (2003) note in passing the im-
migrant advantage in patenting in the 1995 NSCG, and economic historians have studied
the characteristics of nineteenth century inventors (e.g. Khan and Sokoloff 1993).
There is a large literature on the regional determinants of patenting, but the analysis
relies primarily on cross–section variation or qualitative analysis. The literature considers
the effects of private and public R&D spending, the presence of a university, the presence of
small firms, the competitiveness of product markets, the presence of an airport, geographic
centrality, population density and size and the presence of skilled workers, especially
scientists and engineers.4 The most closely related paper is by Zucker and Darby (2006):
they pool data on Bureau of Economic Analysis regions for 1981–2004, and find that
non–university patenting is affected by neither the presence of star scientists, a high wage
(proxying for education) nor a high stock of relevant journal publications (representing
the stock of knowledge).5
Our theoretical analysis shows that workers with science and engineering education are
more likely to emigrate than other (“professional”) skilled workers if the expected wage
premium commanded by professional over unskilled jobs in the destination is smaller than
the cost of adapting professional skills to the destination institutions. We demonstrate
this in Appendix A. Our empirical analysis of the NSCG data shows that immigrants
account for 24% of patents, twice their share in the population, and that the skilled im-
migrant patenting advantage over skilled natives is entirely accounted for by immigrants’
disproportionately holding degrees in science and engineering fields. The data imply that
a one percentage point increase in college–graduate immigrants’ share of the population
increases patents per capita by 6%.
4See, for example, Acs (2002), Bottazzi and Peri (2003), Hicks et al. (2001), and the papers in Acs et
al. (2002); Jaffe, Trajtenberg and Henderson (1993) and successor papers study geographic patterns of
patent citations.5Other relevant papers include Agrawal, Kapur and McHale (2002), who find that emigration from
India reduces access to knowledge in India, Zucker et al. (2006), who examine the determinants of
a region’s publications in nanotechnology, and Marx, Strumsky and Fleming (2007) and Stuart and
Sorenson (2003), who examine the effect of a state’s enforcing non–compete laws on inventor inter–firm
mobility and biotech IPOs respectively.
4
This could overestimate the contribution of immigrants, if immigrants crowd out na-
tives from science and engineering, or could underestimate the contribution, if immigrants
have positive spill–overs. The state panel analysis, which estimates the contribution in-
cluding any spill–overs, shows evidence of positive spill–overs of immigrants, since the
estimates of their impact on patents per capita are higher than in the NSCG: a one per-
centage point rise in the share of immigrant college graduates in the population increases
patents per capita by 9–18%. The state–level results mean that the 1990–2000 increase
in the population share of this group from 2.2% to 3.5% increased patents per capita by
12–21% in a period when patents per capita rose 63%. We find that immigrants who are
scientists and engineers or who have post–college education boost patents per capita more
than immigrant college graduates.
1 Empirical methodology
We use individual–level data to measure and explain differences in patenting behavior
between immigrants and natives, and to gauge the contribution of immigrants to patenting
per capita under the assumption that immigrants do not affect the behavior of natives or
other immigrants. We then use state–level data to estimate the effect of immigrants on
patenting per capita, including any positive or negative spill–overs.
1.1 Individual–level data
A measure of the increase in patenting per capita owing to skilled immigrants can be
calculated as follows.6 Let the skilled immigrant share of patents be α0 (we obtain this
value from the NSCG) and the skilled immigrant share of the population be α1 (we
obtain this value from the census). Let MS be the number of skilled immigrants and
PMS their patents. If the skilled immigrant share of the population increases by one
percentage point, the percent increase in skilled immigrants is ∆MS
MS = 1α1
0.010.99−α1
, the
percent increase in the population is ∆MS
POP= 0.01
0.99−α1and the percent increase in patents
6The full algebra is presented in Appendix B.
5
is ∆PMS
P= 1
PPMS
MS ∆MS = α0∆MS
MS . The percent increase in patents per capita is therefore
1 + ∆PMS
P
1 + ∆MS
POP
− 1 = (0.01)α0 − α1
α1(1− α1). (1)
We shall establish below that skilled immigrants patent more than skilled natives,
and that this difference is driven by the difference in patenting at all. For policy–makers
contemplating reducing skilled immigration and inducing more natives to study science
and engineering, it may be interesting to understand the reasons for the immigrant ad-
vantage. To explore these reasons, we estimate a probit for the probability of having a
patent granted, or the probability of commercializing or licensing a patent, weighted by
the survey weights:
P (patentj) = β0 + β1IMj +Xjβ2 + εj, (2)
where j indexes individuals and IM is a dummy for the foreign–born. The coefficient
of interest is β1. We are interested in how much of the raw patenting gap between
immigrants and natives (the value of β1 with no X covariates) can be explained by adding
the covariates X: field of study of the highest degree, the highest degree, and demographic
variables. We perform the regressions for three samples: college graduates, post–college
degree holders, and scientists and engineers.
1.2 State–level data
We supplement the analysis using a panel of U.S. states with decennial data from 1940–
2000. By extending the period of observation back to 1940, we are able to distinguish
long run and short run effects by differencing the data in lengths varying from ten to 50
years.7 We estimate
∆logPi,t+1
POPi,t+1
= γ0 + γ1∆ISit + γ2∆NSit + ∆Xitγ3 + Zi,1940γ4 + µt + ∆ηit, (3)
where i indexes states, P is the number of patents, POP is state population, IS is the share
of the population or workforce (18–65) composed of skilled immigrants, NS represents the
7Strictly speaking, we should refer to low–frequency and high–frequency effects.
6
corresponding share for skilled natives, Zi,1940 are characteristics of the state in 1940, X
are contemporaneous state characteristics and µt are year dummies. The coefficient of
interest is γ1, though its size relative to γ2 is also of interest. We also present results from
specifications where the dependent variable is not in logs.8
We define a skilled person variously as one with a college degree or more, one with
post–college education, or one working in a science, engineering or computer science oc-
cupation. We include characteristics of the state in 1940 (including land area), to capture
the convergence in patents per capita occurring over the time period. The X covariates
comprise the log of defense procurement spending and the log of the average age of state
residents (18–65). We deliberately do not include R&D spending, as we believe this to
instead be a potential outcome variable. We lead the dependent variable by one year to
allow for a year of research time between the change in the inputs and the patent appli-
cation, as anecdotal evidence suggests the lag can vary between a few months and two
years.
There were several major changes to the patent system between 1980 and 1998 (see
Hall 2005). One change led to a large increase in patenting in electrical engineering
relative to other sectors. To capture potentially differential effects of this by state, we
include among the X’s the share of employment in electrical engineering–related sectors
in 1980, interacted with year dummies.9 Alternatively, we capture this by controlling for
region–specific dummies interacted with a dummy for differences involving years beyond
1980.
We use state populations to weight the regressions,10 since in some small states one
company drives the time series of patenting,11 and we cluster standard errors by state
to allow for serial correlation. Because we account for state fixed effects by estimating
8All patents are filed in Washington D.C.; they are attributed to states based on the home address of
the first inventor.9We use 1980 values as electrical engineering employment was still tiny in most states in 1940–1970.
10Specifically, we weight by 1/(1/popi,t+1 + 1/popi,t−k+1), where k is the length of the difference.11Idaho’s emergence as the state with most patents per capita has been driven by one semi–conductor
company, Micron Technology Inc., founded in 1978, which was granted 1643 patents in 2001 and was the
fourth–ranked company in this regard.
7
equations differenced across time, we elect not to include the change in the patent stock
among the regressors as would be suggested by patent models. Furthermore, because we
analyze long–run changes, we have chosen not to use a partial adjustment model.12
Equation (3) suffers from an endogeneity problem. Skilled workers are likely to migrate
to states which are growing or innovating, causing γ̂1 and γ̂2 to be biased upward in least
squares estimation. On the other hand, γ̂1 in particular could be biased towards zero
owing to measurement error.13 We devise an instrument to address these problems for
skilled immigrants, inspired by a shift–share type analysis of the change in popularity of
a state stemming from changes in the origin regions of skilled immigrants at the national
level.14 To illustrate, if immigrants from Europe prefer the northeastern United States
because it is closer to home and because other Europeans are already there because of
geography, and Asian immigrants prefer the west coast for the same reasons, the large
national increase in the share of skilled immigrants that are Asian will lead to an increase
in skilled immigration to the west coast relative to the northeast. If the national increase
in skilled Asian immigrants is caused by the change in U.S. immigration policy in 1965,
the opening of China to the world in 1979, along with increases in tertiary education in
China and India, it is orthogonal to shocks to west coast patenting.
For a state i, the predicted change in the number of skilled immigrants, caused by
changing origin regions k, can be written as
∆M̂Si =
∑k
Mik
Mk
∆MSk =
∑k
λik∆MSk ,
where λik is state i’s share in 1940 of the national total of immigrants who originate
12We have estimated these models. The coefficient on the change in the stock of patents is close to
one, rendering all other coefficients insignificant, while the coefficient on the partial adjustment term is
insignificant.13There is considerable measurement error for small states in the 1950 census, which was a smaller
sample than later years and which asked certain key questions of only one quarter of the sample. There
is also measurement error for the share of immigrant post–college and immigrant scientists and engineers
in small states in the 1940–70 censuses.14This instrument is similar to the instrument developed by Card (2001). For ∆NS , the change in the
share of native skilled workers, we have experimented unsuccessfully with lagged college enrollments as
an instrument. The enrollment data only begin in the 1970s.
8
from region k, and ∆MSk is the national change in the number of skilled immigrants from
that region. We use 18 source regions or countries, listed in Appendix Table 1. Because
the variable to be instrumented, ∆ISit , is a percentage point change, we convert ∆M̂Si to
percentage points by dividing by the population level at the start of the period to which
∆ refers, to define our final instrument as:
∆M̂Si
POPi.
We deliberately base the λik on immigrants of all educations (and ages) to emphasize
the role of geography and taste and minimize the role of economic factors that might
attract skilled workers specifically. We can control for the λik in the regressions, to ensure
that the instrument is not correlated with the error term due to their omission, and
the year dummies control for all national trends. If controlling for λik and the other
covariates does not account for state–specific patenting shocks which are very persistent
and influence national inflows of particular immigrant groups (e.g. California has serially
correlated positive patenting shocks which caused low–skill Chinese to settle there before
1940 and which incited skilled Chinese to move to the United States in more recent years),
the instrument could be correlated with the error term. We present evidence below that
suggests this is not the case.
Information on Alaska and Hawaii is not available until 1960. If the instrument is con-
structed using the 1960 shares for Alaska and Hawaii instead of the missing 1940 shares,
Hawaii is such an outlier (due to its high share of Asian immigrants in 1960) that the in-
strument does not statistically significantly predict immigration patterns even in weighted
regressions. We therefore drop Hawaii from the analysis entirely, and for simplicity drop
Alaska as well. This makes an imperceptible difference to weighted least squares regres-
sions, and only a small difference to the less preferred unweighted regressions.
9
2 Data and Descriptive Statistics
2.1 Individual–level data
We use the individual–level data from the 2003 National Survey of College Graduates
(NSCG). These data are a stratified random sample of people reporting having a bachelor’s
degree or higher on the long form of the 2000 census. In 2003, all respondents who
had ever worked were asked whether they had applied for a U.S. patent since October
1998, whether they had been granted any U.S. patent since October 1998, and if so, how
many, and how many had been commercialized or licensed.15 The survey will not capture
patents by those with less than a college degree, but we assume that most patents are
captured. Appendix C provides more information on the NSCG. We include in our sample
respondents 65 or younger (the youngest respondent is 23, but few are younger than 26).
Immigrants are those born outside the United States.
We define three (not mutually exclusive) skill categories, motivated in part by con-
sistency with categories that can be distinguished in the censuses: college graduates (i.e.
the full sample); holders of a post–college degree; and those working as scientists and
engineers in the survey week. Only 51% of respondents who had been granted a patent
reported working in a science or engineering occupation. Another 18% reported a man-
agement occupation: a research team’s manager is sometimes listed as a co–inventor on
a patent, and all inventors listed are captured in the data; also, many inventors will have
been promoted to management since obtaining a patent. Science and engineering tech-
nicians represent 2.5% of patent holders, and respondents in health–related occupations
represent another 3.0%.
Table 1 shows details of how patenting varies by immigrant status for the three skill
groups. For college graduates (the whole sample, columns 1–2), 1.9% of immigrants were
granted patents compared to 0.9% of natives, a ratio of 2.1, and patents per capita were
15Questions on patents were also asked in the 1995 NSCG, but only of respondents who said they
worked in research and development in the survey week, which will cause the patents of job changers to
be missed.
10
0.057 for immigrants and 0.028 for natives, a ratio of 2.0. Immigrants therefore patent
at about twice the native rate, with the difference being principally in the probability of
patenting at all. Immigrants held a slightly smaller advantage in patents commercialized
or licensed, patents likely to benefit society more than others: 1.2% immigrants had
commercialized a patent compared to 0.6% for natives, but commercialized patents per
capita were 0.029 for immigrants and 0.017 for natives. The immigrant–native gap is
larger for the sample with post–college education (columns 3–4), but much smaller for
the sample working in science and engineering occupations (columns 5–6). For example,
6.2% immigrants in the latter sample had been granted a patent, compared to 4.9%
natives, and immigrants hold 1.35 times the patents per capita of natives. Appendix
Table 2 contains the means of variables used in the regression analysis below.
2.2 State–level data
The patent data used in the state–level analysis come from the U.S. Patent and Trademark
Office (USPTO). Patents are attributed to states based on the home address of the first
inventor on the patent. We merge a series based on electronic data from 1963 onwards with
a series from paper records for 1883–1976 (see Appendix C for the merging procedure).
Patents are classified according to application (filing) date. Figure 1 shows the evolution
of total patents and patents per 100,000 residents from 1941-2001, our study period.
In Figure 2 we use patent data from 1929 to 2001 to display the long–run convergence
across states in patenting, as measured by changes in the (unweighted) standard deviation
of log patents. The convergence in patents, shown by the downward slope of the top line, is
not merely a function of convergence in population, as is demonstrated by the convergence
in patents per capita (bottom line).16 However, there is divergence in patents per capita
from 1990–2001, and there have historically been other periods of divergence. California
is a force for divergence, as may be seen by the growing gap between the inequality of
state patent counts with California (top line) and without California (middle line).
16Papers such as Co et al. (2006) have previously noted cross–state convergence in patents per capita.
11
We have also used an extract from the Harvard Business School patent data file,
which contains information on patents granted from 1975 to 2007, arranged by year of
application and patent class.17 We have aggregated the patent classes to six categories
using the classification of Hall, Jaffe and Trajtenberg (2001) and our own classification
of patent classes created since 1999. The extract contains the number of citations made
to patents in each patent class, state and application year. These may be viewed as a
proxy for the quality of the patent. We analyze 1971–2001 data using this extract (see
Appendix C for how we approximate 1971 values).
To compute the shares of the population in various education and occupation classes,
to divide these into immigrant and native, and to calculate the average age of the state’s
population, we use the IPUMS microdata of the decennial censuses. Post–college educa-
tion is the highest education level that can be measured consistently throughout 1940–
2000. We define immigrants to be the foreign born. Information for Alaska and Hawaii
is not available in 1940 and 1950, and we elect to drop these states entirely for reasons
explained in the methodology section.
The variable means for the full 1940–2000 sample, weighted by population, are re-
ported in Table 2. Between 1940 and 2000, the share of the population 18–65 composed
of immigrants with college education or more increased twelvefold to 3.5%, while the
equivalent share for post–college increased twelvefold to 1.6%. The population shares
comprising natives with at least college and with post–college increased from 4.1% to
20.0% and from 1.1% to 7.7% respectively. The share of workers composed of immigrant
scientists and engineers multiplied elevenfold to 0.9%, while the native share rose from
0.6% to 3.5%. The Appendix Table 2 contains information about the variables used in
the construction of the instruments.
17We are very grateful to Bill Kerr for making this extract for us.
12
3 Results
3.1 Individual determinants of patenting
The NSCG data may be used to estimate the direct effect of immigration on patenting,
ignoring possible crowd–out or spill–over effects, using equation (1). Immigrants hold
24.2% of patents in the (weighted) data (α0 = 0.242), and in the 2000 census (the basis of
the NSCG sampling frame), college–graduate immigrants were 3.5% of the U.S. population
(α1 = 0.035). A one percentage point rise in the share of college immigrants in the
population therefore implies an increase in patents per capita of 0.061, or 6.1%. The same
exercise may be performed for natives, with the result that a one percentage point rise in
the share of college natives increases patents per capita by 3.5%. As immigrants with post–
college education have 2.0 (=0.112/0.057) times as many patents per capita as immigrants
with only a college degree (see Table 1), the direct impact of an extra percentage point
of post–college immigrants in the population is likely to be 2.0 times higher, or an extra
2.0×6.1 = 12.2%. Similarly, the contribution of an additional percentage point immigrant
scientists and engineers is likely to be 3.1× 6.1 = 18.9%.
To assess the reasons for the immigrant patenting advantage, we first observe that
in Table 1 immigrants’ patenting advantage over natives is much smaller in the scientist
and engineer sample (columns 5 and 6) than in the overall sample (columns 1 and 2).
This suggests that immigrants’ advantage is due in large part to a greater science and
engineering orientation. Table 3 lends further support to this. Column 1 shows that, for
the whole sample, 6.6% of those with a highest degree in physical science and 6.1% of those
with a highest degree in engineering had patented, far ahead of other fields. Column 2
shows a qualitatively similar picture for commercialized or licensed patents. Immigrants’
education is therefore well–suited to patenting, since columns 3 and 4 show that the share
of immigrants with physical science and engineering degrees is more than twice as high
as for natives.
In Table 4, we pursue this explanation using the probit of equation (2) for the prob-
ability of patenting. Column 1 shows that immigrants are 1.0 percentage points more
13
likely to have been granted a patent in the sample of college graduates (top panel), 2.3
percentage points more likely in the sample of post–college educated (second panel) and
1.3 percentage points more likely in the sample of scientists and engineers (third panel).
In the second column, we control for the field of study of the highest degree obtained
by the respondent by adding 30 dummies. For all three samples, the gap becomes small:
6–9% of the original size for college and post–college graduates, and 24% for scientists
and engineers. In the third column, we control for the highest degree obtained by the
respondent. For college graduates and scientists and engineers, the direction of the gap is
reversed: immigrant scientists and engineers are a statistically significant 0.95 percentage
points less likely to patent than natives. Controlling for age, age squared, sex and current
employment status in column 4 changes little. Skilled immigrants’ advantage is therefore
entirely due to the nature of their education, and not to any selection on unobservables
such as ability.18 In columns 5 and 6 we show that the same conclusions may be drawn
for the probability of commercializing or licensing a patent.
3.2 State determinants of patenting
In Table 5, we estimate the state determinants of log patenting per capita using differences
of varying lengths, with a college degree as the measure of skill and least squares estimation
of equation (3). The regression in column 1 is unweighted, while those in the other columns
are weighted. A ten–year difference is taken in columns 1 and 2, a thirty–year difference
in column 3 and a fifty year difference in column 4. The coefficients on the changes in the
immigrant college shares are positive and significant. A one percentage point increase in
the share of the population composed of immigrant college graduates is associated with
a 12–15% increase in patenting per capita. These effects are larger than the 6% impact
calculated based on the NSCG data, implying positive spill–over effects of immigrants.
The coefficients on the change in the share of native college graduates are smaller
than the coefficients for immigrants. The point estimate increases as the difference length
18It is possible that unobservable effects cancel out e.g. immigrants may have higher ability but lower
quality education.
14
increases, and for 50–year differences the coefficient is a significant 5.8 in column 4. The
immigrant/native ratio is 2.6, somewhat larger than the 1.9 ratio in the NSCG. The
coefficient suggests that skilled natives too have positive spill–overs, as the effect of a one
percentage point increase in their population share based on the NSCG data was 3.5%.
The absence of significance at short differences probably reflects the emphasis of short
differences on high–frequency events (Baker, Benjamin and Stanger 1999), since the share
of native college graduates changes only gradually.
Older populations appear to be more innovative, as indicated by the positive coeffi-
cients on the average age of the state. This may reflect the importance of management or
other skills complementary to innovation. As suggested by time series work in Griliches
(1990), Department of Defense procurement spending lowers patenting, presumably in
part because military invention is primarily protected by secrecy rather than patents. Fi-
nally, the importance of the 1940 conditions (and land area) increases with the difference
length, and the coefficients indicate that patent growth was lower for initially richer and
more densely populated states.
We reproduce key Table 5 results in Table 6 Panel A columns 1–2, to facilitate their
comparison with the equivalent coefficients for post-college education (Panel B) and sci-
entists and engineers (Panel C). The coefficients for immigrant post–college are 20.7 and
29.8 in columns 1 and 2, 1.6–2.0 times as high as for immigrant college graduates, com-
pared to a ratio of 2.0 the NSCG data. The coefficients indicate positive spill–overs, as
the effect of a one percentage point increase in the immigrant post–college share in the
individual data was 12%. The coefficients for the share of native post–college educated
are not statistically significant, though the point estimates are higher for the longer dif-
ferences, yielding an immigrant/native ratio of 3.5 at 50–year differences compared to 3.1
in the NSCG. For scientists and engineers in panel C columns 1–2, a one percentage point
increase raises patents by 52 log points. This is high compared with the direct NSCG
effect of about 19% and compared with the effect of natives at 50–year differences (25
log points), given that in the NSCG the immigrant patenting advantage over natives was
only 35% amongst scientists and engineers. We return to this discrepancy below.
15
In columns 3 and 4 we repeat the regressions of columns 1 and 2, using the unlogged
dependent variable and reporting coefficients multiplied by 100. For immigrants, the
50–year difference yields smaller coefficients than the ten–year difference. For immigrant
college graduates in Panel A, a one percentage point increase in their share is associated
with a 0.000037 (column 3) or 0.000027 (column 4) increase in patents per capita, which
represent respectively 16.1% and 11.7% increases compared to the mean, close to the
estimates in columns 1 and 2. The coefficients for post–college immigrants (Panel B) are
1.9–2.0 times the magnitude of the college immigrant coefficients, as we would expect,
but are statistically insignificant. The disparity between ten and 50–year differences is
large for the regressions using scientists and engineers (Panel C). The 50–year coefficient
is similar in magnitude to the results from the log specification: the coefficient of 1.35
(column 4) means that a one percentage point increase in the skilled immigrant share is
associated with a 58.7% increase compared to the mean. The skilled immigrant coefficients
in columns 3–4 are not very sensitive to the covariates included, while the results in
columns 1–2 are much smaller if the 1940 covariates (including land area) are not included.
We have repeated all the least squares regressions of Table 6 splitting the skilled
natives according to whether they lived in the state of their birth or not (these results
are not reported). For long differences, it is the coefficient on the change in the share of
skilled natives born in another state that is larger and statistically significantly positive.
For short and medium differences, which coefficient is more larger depends on the skill
group.
Before presenting instrumental variables results, we display in Figure 3 the correla-
tion between the change in the immigrant college share and its instrument (the predicted
change) for each decade, and plot the weighted regression line. If the instrument were
picking up shocks to patenting from around 1940, we would expect the instrument to grad-
ually weaken over time. Instead, the instrument is weak in the low immigration decades
of 1940–1950 and 1950–1960, strong thereafter. The unreported figures for immigrant
post–college and scientist and engineer shares indicate similar correlations, though they
are less significant for scientists and engineers.
16
We now proceed to present the results of instrumental variables estimation and other
specification checks, focusing on the log specification and ten–year differences, and re-
porting only the coefficient on the change in the skilled immigrant share. For conciseness
we present the full results only for the case of college proxying for skill, in Table 7. Row 1
shows that in the base specification, instrumental variables increases the coefficient to
30, more than twice the least squares coefficient of 13. The instrument is strong in the
first stage, as indicated by the value in brackets of 27 for the F–statistic for the excluded
instrument’s significance in the first stage (the first stage itself, along with all other first
stages for the table, is shown in Appendix Table 3). The higher magnitude of the instru-
mental variables estimate may indicate that in least squares, measurement error’s bias
towards zero is more important than upward bias due to the endogenous location choice
of immigrants, a possibility mooted by Card and DiNardo (2000) in a similar context.
It seems less likely that skilled immigrants whose behavior is affected by the instrument
(skilled immigrants whose location decision is affected by historical geographic or taste
considerations) are more inventive than other immigrants.
In rows 2 and 3 we check the robustness of the results to different samples. Without
California (row 2), the least squares estimate falls from 13.2 to 9.2 and the instrumental
variables estimate from 30 to 26. Without differences involving the year 2000, the point
estimates fall more. In row 4 we return to the full sample and add seven dummies for
BEA regions, which pick up region–specific trends in per capita patenting. This decreases
the point estimates compared to row 1. The region coefficients are jointly significant,
as are the coefficients for all sets of covariates we add in this table. In row 5, we use
state instead of region dummies, which mainly serves to increase the standard errors. In
row 6, we revert to using BEA region dummies, and add controls for the share of workers
in electrical engineering in 1980 interacted with year dummies, which decreases the least
squares estimate from 11.5 in row 4 to 9.6, but leaves the instrumental variables estimate
little changed at 23.
Until this point, the regressions have not controlled for the state’s 1940 shares of the
eighteen immigrant groups that enter the calculation of the instruments (λik). We add
17
these shares to the controls in row 7, which increases the coefficients slightly as well as the
standard errors, rendering the least squares estimate insignificant. As the point estimates
change little, we do not include the 1940 shares in the remaining rows.
Since the change in the native skilled share is endogenous, the instrumental variable
estimate of the effect of the change in the immigrant skilled share is only unbiased if the
two variables are independent. Since this is obviously not the case (the correlation in the
first stage is significantly negative), we experiment in row 8 with dropping the control
for the change in the share of college natives. Compared to row 6, the least squares
coefficient falls slightly, but the instrumental variables coefficient falls considerably, from
23.1 to 17.6.
In row 9 we propose a more parsimonious specification aimed at capturing post–1980
patenting changes, adding to the base specification only BEA region dummies interacted
with a dummy for post–1980 (i.e. for differences including 1990 or 2000). These results
are very close to those of row 8, although the addition of these covariates has weakened
the instrument considerably in the first stage, as evidenced by the fall in the F–statistic
in brackets. In row 10 we drop the change in the native college share from the covariates
of the row 9 specification, and the estimates fall to the lowest values in the table: 7.0 for
least squares and 12.3 for instrumental variables.
Our preferred specifications for least squares are rows 6 and 9 (which include the native
skilled share), while for instrumental variables they are the counterparts excluding the
native skilled share in rows 8 and 10. We present their results in Table 8 for all three
skill groups (repeating the college results). For immigrant college graduates (columns 1
and 2), a one percentage point increase in share increases patenting per capita by 8–10%
in least squares and 12–18% in instrumental variables, more than the 6% based on the
individual–level data (statistically significantly so in the case of the highest coefficient),
and therefore implying positive spill–overs. For post–college immigrants (columns 3 and
4), the upper specifications lead to insignificant coefficients similar in size to the college
coefficients: 11.3 and 18.9 for least squares and instrumental variables respectively. It
seems implausible that the effects would not be larger than for college immigrants (and this
18
specification is unusual in this regard), so we put more weight on the lower specifications
which yields coefficients of 15.9 and 27.0, about double the college coefficients, as would
be expected from the individual–level analysis. The individual–level effect calculated for
the immigrant post–college share was 12%, so overall the coefficients imply considerable
positive spill–overs.
We do not present instrumental variables results for immigrant scientists and engineers,
as the instrument is too weak in the first stage, but the least squares coefficients in
column 5 are 38.2 and 30.7 (significant only at the 10% level), compared to a 19% effect
calculated with the individual–level data. The scientist and engineer coefficients are 3.7–
4.0 times their college counterparts in column 1, which still seems slightly high compared
to the ratio of 3.1 in the individual–level data. For immigrant scientist and engineers in
the specifications of this table, contrary to the cases of immigrant college and post–college,
the coefficient on the share generally falls as the difference length increases. This means
that at longer differences, the immigrant and native shares of scientists and engineers
have similar coefficients, as would be expected based on the individual–level results. For
example, in the 50–year counterpart to the upper specification of Table 8, the coefficient
on the immigrant scientist and engineer share is 27.0 (standard error 16.2) while the native
coefficient is 22.9 (standard error 5.8). These values imply ratios of immigrant to native
and of immigrant scientists/engineers to immigrant college very similar to in the NSCG.
The instrument is also more powerful at this long difference (an F–statistic of 11 in the
first stage), and the instrumental variables coefficient is 61.4 (standard error 28.7). These
are our preferred coefficients for scientists and engineers.
In Table 9 we investigate further using the Harvard Business School patent data for
1971–2001. In row 1 we repeat the least squares base specification for log patents per
capita for this smaller sample, and obtain slightly smaller point estimates for immigrant
college (10.7), post–college (15.2) and scientists and engineers (45.7) compared to those
in Table 6. In row 2 we change the dependent variable to be the log of patent citations
per capita, and in row 3 we add region dummies to this specification. The results are
not very different from the results for patent counts, suggesting immigrants are not gen-
19
erating patents of lower quality than native patents. Unreported instrumental variables
coefficients are larger (21 for college graduates in the base specification) but insignificant.
In rows 4–9 we present the results for the six categories of patent. The standard errors
are high when the data are split in this way, and we elect simply to present the least squares
base specification rather than various specifications with insignificant coefficients. From
the reported results as well as the unreported results, the only firm conclusions are that
there is no effect for mechanical patents, and a negative effect for “other” patents. The
beneficial effects of immigration are therefore spread across computer and communications
patents, electrical and electronic patents, drug and medical patents, and chemical patents.
4 Conclusions
In this paper we have combined individual and aggregate data to demonstrate the im-
portant boost to innovation provided by skilled immigration to the United States in
1940–2000. A calculation for 1990–2000, when patenting per capita rose 63%, puts the
magnitudes of the effects in context. The 1.3 percentage point increase in the share of
the population composed of immigrant college graduates and the 0.7 percentage point
increase in the share of post–college immigrants both increased patenting per capita by
about 12% based on least squares19 and 21% based on instrumental variables. The 0.45
percentage point increase in immigrant scientists and engineers increased patenting per
capita by about 13% based on least squares20 and 32% based on instrumental variables.
These impacts include the positive spill–overs of skilled immigrants, which are a substan-
tial share of the total impact: calculations based on individual–level data of the impacts
without spill–overs suggest impacts of about 8–9% for all three skill groups.21
We find that a college graduate immigrant contributes at least twice as much to
patenting as his or her native counterpart. The difference is fully explained by the greater
19College: Table 8 column 1 average coefficient 9.0, 9.0 × 1.3 = 11.7 log points= 12%; Post–college:
Table 8 column 3 coefficient 15.9, 15.9× 0.7 = 11.1 log points = 12%.20Coefficient 27.0 from text, 27.0× 0.45 = 12.1 log points= 13%.216.1%× 1.3 = 7.9%; 12.2%× 0.7 = 8.5%; 18.9%× 0.45 = 8.5%
20
share of immigrants with science and engineering education, implying immigrants are
not innately more able than natives. Indeed, immigrants are less likely to have patented
recently than observably similar native scientists and engineers. Despite this, the fact that
immigrants increase patenting per capita shows that their presence in the United States
provides a previously uncharacterized benefit to natives, assuming the immigrants would
have been less innovative or less able to commercialize their innovation elsewhere or that
U.S. natives benefit more from innovation and commercialization in the United States
than abroad. We can make a crude calculation of the benefit using the results of Furman,
Porter and Stern (2002), who find that the elasticity of a country’s GDP with respect
to its patent stock is 0.113, controlling for capital and labor. This elasticity implies that
the influx of immigrant college graduates in the 1990s increased U.S. GDP per capita by
1.4–2.4%.
One should be cautious in drawing the conclusion that innovation could be sustained
by simultaneously subsidizing natives to study science and engineering and cutting im-
migration of scientists and engineers. The additional natives drawn into science and
engineering might have lower inventive ability than the excluded immigrants, and such
natives might have contributed more to the U.S. economy outside science and engineering.
While evidence in the paper of positive spill–overs from scientists and engineers appears to
support the dual policies of subsidizing native science and engineering study and increas-
ing immigration of scientists and engineers, it is possible that members of other skilled
professions provide equally large spill–overs that are simply more difficult to measure.
Finally, the paper leaves for future research the question of which immigration pathways
lead to the most successful immigrants: for example, admitting science and engineering
graduate students and facilitating their remaining in the United States after graduation
compared with admitting more scientists and engineers on temporary work visas.
21
References
Acs, Zoltan J., 2002. Innovation and the Growth of Cities, Northampton, M.A.: EdwardElgar.
Acs, Zoltan J., Henri L.F. de Groot and Peter Nijkamp eds. 2002. The Emergence of theKnowledge Economy, Berlin: Springer Verlag.
Aghion, Philippe and Peter Howitt. 1992. “A Model of Growth through Creative Destruc-tion”. Econometrica, 60 pp. 323–351.
Agrawal, Ajay, Devesh Kapur and John McHale. 2007. “Brain Drain or Brain Bank?The Impact of Skilled Emigration on Poor–Country Innovation”. University of Torontoworking paper.
Anderson, Stuart and Michaela Platzer. 2006. “American Made: The Impact of ImmigrantEntrepreneurs and Professionals on U.S. Competitiveness”. National Venture CapitalAssociation.
Baker, Michael, Dwayne Benjamin and Shuchita Stanger. 1999. “The Highs and Lows ofthe Minimum Wage Effect: A Time–Series Cross–Section Study of the Canadian Law”.Journal of Labor Economics, 17 (2) pp. 318–350.
Borjas, George J. 2006. “Do Foreign Students Crowd Out Native Students from Gradu-ate Programs?”. In Ronald G. Ehrenberg and Paula E. Stephan eds. Science and theUniversity, Madison: University of Wisconsin Press.
Bottazzi, Laura and Giovanni Peri. 2003. “Innovation and spillovers in regions: Evidencefrom European patent data”. European Economic Review, 47 pp. 687–710.
Card, David. 2007. “How Immigration Affects U.S. Cities”. CReAM Discussion Paper No.11/07.
Card, David. 2005. “Is the New Immigration Really So Bad?” Economic Journal, 115(507) pp. F300–323.
Card, David. 2001. “Immigrant Inflows, Native Outflows and the Local Labor MarketImpacts of Higher Immigration”. Journal of Labor Economics 19 (1) pp. 22–64.
Card, David and John DiNardo. 2000. “Do Immigrant Inflows Lead to Native Outflows?”American Economic Review Papers and Proceedings, 90 (2) pp. 360–367.
Chellaraj, G. Keith E. Maskus and A. Mattoo. 2008. “The Contribution of Skilled Immi-gration and International Graduate Students to U.S. Innovation”. Review of Interna-tional Economics, 16 (3) pp. 444–462.
Chiswick, Barry and Sarinda Taengnoi. 2007. “Occupational Choice of High Skilled Im-migrants in the United States”. International Migration, 45 (5) pp. 3–34.
22
Co, Catherine Y., John S. Landon–Lane and Myeong–Su Yung. 2006. “Inter–State Dy-namics of Invention Activities, 1930–2000”. Journal of Applied Econometrics, 21 pp.1111–1134.
Furman, Jeffrey L., Michael E. Porter and Scott Stern. 2002. “The determinants of na-tional innovative capacity”. Research Policy, 31 pp. 899–933.
Griliches, Zvi. 1990. “Patent Statistics as Economic Indicators: A Survey”. Journal ofEconomic Literature, 28 (4) pp. 1661–1707.
Grossman, Gene and Elhanan Helpman. 1991a. Innovation and Growth in the GlobalEconomy, Cambridge: MIT Press.
Grossman, Gene and Elhanan Helpman. 1991b. “Quality Ladders in the Theory ofGrowth”. Review of Economic Studies, 58 pp. 43–61.
Hall, Bronwyn H. 2005. “Exploring the Patent Explosion”. Journal of Technology Trans-fer, 30 (1/2) pp. 35–48.
Hall, Bronwyn H., Adam Jaffe and Manuel Trajtenberg. 2001. “The NBER Patent Ci-tation Data File: Lessons, Insights and Methodological Tools”. NBER Working Paper8498.
Hicks, Diana, Tony Breitzman, Dominic Livastro and Kimberly Hamilton. 2001. “Thechanging composition of innovative activity in the US – a portrait based on patentanalysis”. Research Policy, 30 pp. 681–703.
Jaffe, Adam B., Manuel Trajtenberg and Rebecca Henderson. 1993. “Geographic Local-ization of Knowledge Spillovers as Evidence by Patent Citations”. Quarterly Journal ofEconomics, 108 (3) pp. 577–598.
Jones, Charles I. 1995. “Time Series Tests of Endogenous Growth Models”. QuarterlyJournal of Economics, 110 (2) pp. 495–526.
Kerr, William R. 2007. “The Ethnic Composition of US Inventors”. Harvard BusinessSchool Working Paper No. 08-006.
Kerr, William R and William Lincoln. 2008. “The Supply Side of Innovation: H–1B VisaReforms and U.S. Ethnic Invention”. Harvard Business School working paper.
Khan, B. Zorina and Kenneth L. Sokoloff. 1993. “Schemes of Practical Utility: En-trepreneurship and Innovation Among Great Inventors in the United States, 1790–1865”. Journal of Economic History, 53 (2) pp. 289–307.
Marx, Matt, Deborah Strumsky and Lee Fleming. 2007. “Noncompetes and InventorMobility: Specialists, Stars, and the Michigan Experiment”. Harvard Business SchoolWorking Paper 07-042.
23
Morgan, Robert P., Carlos Kruytbosch and Nirmala Kannankutty. 2001. “Patenting andInvention Activity of U.S. Scientists and Engineers in the Academic Sector: Compar-isons with Industry”. Journal of Technology Transfer, 26 pp. 173–183.
Niebuhr, Annekatrin. 2006. “Migration and Innovation: Does Cultural Diversity Matterfor Regional R&D Activity?” IAB Discussion Paper No. 14/2006.
Paserman, Daniele M. 2008. “Do High–Skill Immigrants Raise Productivity? Evidencefrom Israeli Manufacturing Firms, 1990–1999”. IZA Discussion Paper 3572.
Peri, Giovanni. 2007. “Higher Education, Innovation and Growth”. In Giorgio Brunello,Pietro Garibaldi and Etienne Wasmer eds. Education and Training in Europe, Oxford:Oxford University Press.
Peri, Giovanni and Chad Sparber. 2008. “Highly Educated Immigrants and OccupationalChoice” U.C. Davis working paper.
Romer, Paul M. “Endogenous Technological Change”. Journal of Political Economy, 98pp. S71–103.
Stephan Paula E. and Sharon G. Levin. 2001. “Exceptional contributions to US scienceby the foreign–born and foreign–educated”. Population Research and Policy Review, 20pp. 59–79.
Stuart, Toby E. and Olav Sorenson. 2003. “Liquidity Events and the Geographic Dis-tribution of Entrepreneurial Activity”. Administrative Science Quarterly, 48 (2) pp.175–201.
Stuen, Eric T., Ahmed Mushfiq Mobarak and Keith E. Maskus. 2007. “Foreign PhD Stu-dents and Knowledge Creation at U.S. Universities: Evidence from Enrollment Fluctu-ations”. University of Colorado working paper.
U.S. Department of Commerce, Patent and Trademark Office. 1977. Technology Assess-ment and Forecast, Seventh Report, Washington, D.C.
Wadhwa, Vivek, AnnaLee Saxenian, Ben Rissing and Gary Gereffi. 2007. “America’s NewImmigrant Entrepreneurs”. Kauffman Foundation report.
Zucker, Lynne G. and Michael R. Darby. 2006. “Movement of Star Scientists and Engineersand High–Tech Firm Entry”. NBER Working Paper 12172.
Zucker, Lynne G., Michael R. Darby, Jonathan Furner, Robert C. Liu and Hongyan Ma.2006. “Minerva Unbound: Knowledge Stocks, Knowledge Flows and New KnowledgeProduction”. NBER Working Paper 12669.
24
Appendix A: Theory
A.1 Model
The occupations of skilled immigrants to the United States depend in part upon thechoices of potential immigrants, even if other factors are also at work. U.S. employersand universities, for example, influence the allocation of visas. Also, scientists and en-gineers might be common among immigrants because market conditions in the sendingcountries lead a larger share of foreigners than Americans to study science and engineer-ing. Nevertheless, it is likely that self–selection is in part responsible for the fact thatskilled immigrants of all visa types are more likely than skilled natives to have studiedscience and engineering (as shown by the National Survey of College Graduates).
We consider a world with two countries, the origin o and the potential destinationd, and three types of labor Lk: scientific labor Ls, professional labor Lp and unskilledlabor Lu. We assume that wages for each type of labor are higher in country d, so thatimmigration goes in one direction only: wdk > wok for all k. The migration cost is Md
with a distribution g(Md) on [MdL,M
dH ]. The cost may vary for an individual for many
reasons such as relatives in the destination country, number of children, language skills,adaptation capacity, etc.
Consider the decision of an origin worker to emigrate. If she chooses to stay in theorigin country, a worker of skill category k will receive a real net wage wok with certainty.Workers of all three skill categories can find an unskilled job with certainty if they moveto country d, but professional migrants can only find a professional job in country d withprobability P d
pp, and scientific migrants can only find a scientific job with probability P dss
(and scientific workers cannot work as professionals and vice–versa). Moreover, whilescientific knowledge is equivalent in the two countries, a professional migrant needs toadapt her skills at cost Cd
p > 0 in order to get a professional job in country d. Thus,P dpp = 0 unless the worker adapts her skills.
We assume workers are risk neutral, have perfect access to credit, care only aboutconsumption, and therefore maximize the expected present value of lifetime income. Theexpected wage of an worker in the origin country is
E[w|k] = P (emigrate to d)[E(wd|k)−Md|emigrate to d]+(1−P (emigrate to d))wok, (4)
where P (emigrate to d) is the probability of migration. Assuming that the worker prefersthe status quo in case of indifference, she will migrate if
E(wd|k)−Md > wok ⇐⇒ Γdk ≡ E(wd|k)− wok > Md. (5)
Thus, the worker will emigrate to country d with probability G(Γdk). The expected gainfrom emigration to country d for unskilled workers is
Γdu = wdu − wou, (6)
25
for professional workers is
Γdp =
E[wd|k=p]︷ ︸︸ ︷max{wdu, P d
ppwdp + (1− P d
pp)wdu − Cd
p}−wop= wdu + max{0, P d
pp(wdp − wdu)− Cd
p} − wop (7)
= wdu − wou + max{0, P dpp(w
dp − wdu)− Cd
p} − wop + wou
= Γdu +max{0, P dpp(w
dp − wdu)︸ ︷︷ ︸
Expected productive skill premium in country d
−Cdp}
︸ ︷︷ ︸Net expected productive skill premium in country d
− (wop − wou)︸ ︷︷ ︸Productive skill premium at home
,
and for scientific workers is
Γds =
E[wd|k=s]︷ ︸︸ ︷P dssw
ds + (1− P d
ss)wdu−wos
= wdu + P dss(w
ds − wdu)− wos (8)
= wdu − wou + P dss(w
ds − wdu)− wos + wou
= Γdu + P dss(w
ds − wdu)︸ ︷︷ ︸
Net expected innovative skill premium in country d
− (wos − wou)︸ ︷︷ ︸Innovative skill premium at home
.
We assume that the cost of acquiring professional and scientific skills is the same, andthat the expected benefits must therefore be the same. If this were not the case, workersin the origin country would all choose the more profitable skill category. This woulddecrease the marginal value of labor of this category, and thus its wage, until equality wasattained again. Therefore, we have
G(Γds)E(Γds −Md|Md < Γds) + wos = G(Γdp)E(Γdp −Md|Md < Γdp) + wop, (9)
which can be rearranged as
G(Γds)E(Γds −Md|Md < Γds)−G(Γdp)E(Γdp −Md|Md < Γdp) = wop − wos . (10)
Let ϕ(Γdk) ≡ G(Γdk)E(Γdk−Md|Md < Γdk). Noting22 that∂ϕ(Γd
k)
∂Γdk> 0 (strict inequality if
Γdk > IdL), we have that Γds −Γdp is of opposite sign from wos −wop. We can use this to showthat, under some conditions, we must have Γds > Γdp i.e. a greater return to migration forscientific than professional workers.
Proposition 1. If wdu < wos, then a necessary condition that Γds > Γdp is
Ppp(wdp −wdu)−Cd
p <1
G(Γdp)[(wos −wop)[1−G(Γdp)] + φ(Γdp)− φ(Γds) +G(Γds)Pss(w
ds −wdu)],
and a sufficient condition isCdp > Ppp(w
dp − wdu).
22For the proof, see below.
26
Proof. See below.
Focusing on the simpler sufficient condition, we see that for an origin country whosescientific workers earn more at home than unskilled workers in the destination, scientificworkers have a larger expected gain from migration than professional workers if the skilladaptation costs for professional migrants are larger than the expected professional skillpremium in the destination. Therefore, scientific workers are more likely to migrate thanprofessional workers. No correspondingly simple condition exists for the case of wdu > wos ,where unskilled workers in the destination earn more than scientific workers in the origincountry.23
A.2 Proof of Proposition 1
Proposition 1. If wdu < wos, then a necessary condition that Γds > Γdp is
Ppp(wdp −wdu)−Cd
p <1
G(Γdp)[(wos −wop)[1−G(Γdp)] + φ(Γdp)− φ(Γds) +G(Γds)Pss(w
ds −wdu)],
and a sufficient condition isCdp > Ppp(w
dp − wdu).
Proof. This is a proof by contradiction. First, replace (7) and (8) in (9). This gives
G(Γds)[Γdu + Pss(w
ds − wdu)− (wos − wou)− E(Md|Md < Γds)] + wos =
G(Γdp)[Γdu + max{0, Ppp(wdp − wdu)− Cd
p} − (wop − wou)− E(Md|Md < Γdp)] + wop.
Using (6) and rearranging, we get
G(Γds)[wdu + Pss(w
ds − wdu] + [1−G(Γds)]w
os − φ(Γds) =
G(Γdp)[wdu + max{0, Ppp(wdp − wdu)− Cd
p}] + [1−G(Γdp)]wop − φ(Γdp),
whereφ(Γdk) ≡ G(Γdk)E(Md|Md < Γdk).
Also, using the Fundamental Theorem of Calculus, we have that∂φ(Γd
k)
∂Γdk> 0.
Adding and subtracting G(Γdp)wos on the right side and rearranging gives
(wdu − wos)[G(Γds)−G(Γdp)] = (wop − wos)[1−G(Γdp)] + φ(Γds)− φ(Γdp)
+G(Γdp) max{0, Ppp(wdp − wdu)− Cdp} −G(Γds)Pss(w
ds − wdu).
23In principle, we can maximize discounted lifetime income of workers in the origin country, takingthe migration option into account and assuming a distribution of the cost of skilled education relative tounskilled education, and calculate the share of workers at each skill level, for migrants and non–migrants.In practice, the resulting non–linear equations cannot be solved analytically.
27
Now, suppose that wdu < wos and Γdp > Γds. We have that the left side of the equation ispositive, since G(�) is a density function, so it is increasing. Now, let us look at the rightside of the equation. We have:
(wop − wos)︸ ︷︷ ︸60, since Γd
p>Γds
[1−G(Γdp)]︸ ︷︷ ︸>0, since G(�) is a density︸ ︷︷ ︸60
+φ(Γds)− φ(Γdp)︸ ︷︷ ︸60, since Γd
p>Γds
+G(Γdp) max{0, Ppp(wdp − wdu)− Cdp} −G(Γds)Pss(w
ds − wdu)︸ ︷︷ ︸
<0, else, no one wants skilled job
.
Therefore, the right side is negative if
max{0, Ppp(wdp − wdu)− Cdp} <
1
G(Γdp)[(wos − wop)[1−G(Γdp)] + φ(Γdp)− φ(Γds) +G(Γds)Pss(w
ds − wdu)]︸ ︷︷ ︸
>0
.
Thus, a necessary condition to have the right side negative is
Ppp(wdp −wdu)−Cd
p <1
G(Γdp)[(wos −wop)[1−G(Γdp)] + φ(Γdp)− φ(Γds) +G(Γds)Pss(w
ds −wdu)],
and a sufficient condition isCdp > Ppp(w
dp − wdu).
Under these conditions, we get a contradiction, since the left side is strictly positive,but the right side is negative. As long as either of these conditions holds, we must haveΓdp < Γds if wdu < wos .
A.3 Proof that ∂ϕ(Γdk)/∂Γd
k ≥ 0
Proof. We will show that ∂ϕ(Γdk)/∂Γdk ≥ 0 with strict inequality if Γdk > MdL, where Md
L
is the lower bound on immigration cost. First, note that
ϕ(Γdk) = G(Γdk)E(Γdk −Md|Md < Γdk) =
∫ Γdk
MdL
(Γdk −Md)g(Md)dMd
= Γdk
∫ Γdk
MdL
g(Md)dMd
︸ ︷︷ ︸G(Γd
k)
−∫ Γd
k
MdL
Mdg(Md)dMd
︸ ︷︷ ︸φ
∂ϕ(Γdk)/∂Γk = G(Γdk) + Γkg(Γdk)− ∂φ/∂Γdk︸ ︷︷ ︸=Γkg(Γ
dk) using Fundamental Theorem of Calculus
= G(Γdk) ≥ 0, since G(.) is a density function
28
Appendix B: Algebra for Equation (1)
If immigrants’ share of the population grows by one percentage point,
MS + ∆MS
POP + ∆MS− MS
POP= 0.01,
which implies after some rearranging that
∆MS =0.01POP
0.99POP −MS.
Therefore, the percent increase in the population can be calculated as
∆MS
MS=POP
MS
0.01
0.99− MS
POP
=1
α1
0.01
0.99− α1
.
The percent increase in the population is
∆MS
POP=
0.01
0.99− MS
POP
=0.01
0.99− α1
. (11)
We calculate the percent increase in patents assuming that the additional immigrantscontinue to patent at rate PMS
MS :
∆PMS
P=
1
P
PMS
MS∆MS = α0
∆MS
MS. (12)
The expressions (11) and (12) can then be substituted into the expression for the percentincrease in patents per capita on the left hand side of equation (1) to obtain the expressionon the right hand side.
29
Appendix C: Data
C.1 National Survey of College Graduates
The data were collected between October 2003 and August 2004 by the U.S. Bureauof the Census, on behalf of the National Science Foundation. The data consist of astratified random sample of people reporting having a bachelor’s degree or higher on thelong form of the (April) 2000 census, who were under age 76 and living in the UnitedStates or its territories including Puerto Rico in the reference week of October 1, 2003.We drop respondents living outside the United States and define as immigrants thoseborn outside the United States. Missing information is imputed with a hot deck pro-cedure, and imputed values are not flagged. More information on the data is providedat www.nsf.gov/statistics/showsrvy.cfm?srvy CatID=3&srvy Seri=7#fn1. The data areavailable at www.nsf.gov/statistics/sestat/.
C.2 Patents
We combine two patent series from the U.S. Patent and Trademark Office. The firstseries was compiled for me by the USPTO based on their electronic records which beginin 1963. This series is utility patents by state and year of application. Year of applicationis preferred to year of grant as it is a more accurate match to the time of invention. Thesecond series (U.S. Department of Commerce 1977) is from paper–based USPTO recordsof patents by state and grant year 1883–1976 (application year is not available pre–1963).Grants lag applications by a median of three years between 1950 and 1963 (accordingto our US–wide calculations based on Lexis–Nexis), so we lead this series three years.Patents grants are also more volatile than patent applications (Hall 2005), so we smooththe series with a three year moving average. Finally, because for 1930–1960 plants anddesigns cannot be separated from utility patents, we leave them in for the whole series,calculate by state the average percent gap in the overlap years of the two series (18% onaverage), and reduce the old series by this percent. We then merge the series, using theadjusted paper series values only for pre–1963. The USPTO attributes a patent to a stateaccording to the home address of the first–listed inventor.
We have also used an extract from the Harvard Business School patent data file, whichcontains information on utility patents granted from 1975 to 2007, arranged by year ofapplication and patent class. We have aggregated the patent classes to six categoriesusing the classification in Hall, Jaffe and Trajtenberg (2001) and our own classificationof patent classes created since 1999. In particular, we attribute classes 506 and 977 tochemical patents; classes 398, 701–720, 725 and 726 to computers and communicationpatents; and classes 901 and 903 to mechanical patents. We have not been able to finddefinitions for some patent classes created in 2006 or later (which affects some patentsapplied for in earlier years), and a small number of patents have a missing patent class.For the application years we used, 0.04% of patents are not allocated to one of our sixcategories. To examine patents by category, we have simply attributed 1974 values (mostpatents granted in 1975 were applied for in 1974 or earlier) to 1971, then used 1971, 1981,
30
1991 and 2001 patent values, and 1970, 1980, 1990 and 2000 values for the dependentvariables. Some small states do not have patents in every category in every year, and inthe analysis of log patents these observations are missing.
The extract also contains the number of citations made to patents in each patentclass, state and application year. These may be viewed as a proxy for the quality of thepatent. We calculate citations per patent from 1974 onwards for each state. We then runa regression of this ratio on a trend for each state from 1974–1980, and use the resultingcoefficient to predict the 1971 value of citations per patent for each state. We then returnto our original, longer patent series obtained directly from the USPTO, and multiply thepatents by the ratio for 1971 onwards. We can then study citations, or quality–adjustedpatents, for 1971, 1981, 1991 and 2001.
C.3 Immigration, education, age, occupation, labor force status
We use extracts from the Integrated Public Use Microdata Series for the United StatesCensus, available at usa.ipums.org/usa/, and aggregate to the state level using the weightsprovided. Variables computed as shares (other than the excluded instruments) are com-puted as shares of the population or workers aged 18–65, and average population age isthe average age of people aged 18–65. Immigrants are people born outside the UnitedStates. We use the census–provided edurec variable to identify college graduates (16 yearsof education or more in the 1940–1980 censuses, and a college or higher degree in the 1990and 2000 censuses) and high–school dropouts (11 or fewer years of education). Peoplewith post–college education are people with 17 or more years of education in the 1940–1980 censuses, and a post–college degree in 1990 and 2000. This is the highest level ofeducation that can be distinguished for the whole 1940–2000 period. Alaska and Hawaiiare not in the 1940 and 1950 IPUMS and we drop them from the analysis. The SIC codeswe count as electrical engineering are 321, 322, 342, 350, 371, 372.
C.4 Other data
We use Bureau of Economic Analysis data for total state population (used to weight theregressions) and for state personal income per capita (available from 1929 onwards, unlikegross state product which is not available for our whole period). The data are availableat www.bea.gov/regional/spi/.
Department of Defense procurement contracts by state are available on paper for theearly years in Prime Contract Awards by State, Fiscal Years 1951–1978, published by theDepartment of Defense, OASD (Comptroller), Directorate for Information Operationsand Control. The later years are available online at www.fpds.gov. Some measurementerror in the attribution to states is involved, as recipient firms may subcontract the workto firms in other states. Also, in the electronic records for 1978–1983, 1986 and 1989 (ofwhich only 1980 is relevant for the paper), the California numbers seem to be too small bya factor of 1000, so we have multiplied them by 1000. (We have obtained scanned versionsof the paper documents for these years: the values for the non–problematic states and
31
years are only approximately the same as those online, but the problematic Californiayears are indeed about 1000 times higher than the online version.) We attribute the1951 value to 1950, and set changes in the values involving 1940, for which data are notavailable, to zero.
We obtain the land area of each state from the US. Census Bureau atwww.census.gov/population/censusdata/90den stco.txt.
32
Table 1: Patenting by immigrant status (1) (2) (3) (4) (5) (6) College graduates Post-college graduates Scientists and
engineers Immigrant Native Immigrant Native Immigrant Native Any patent granted 0.019 0.009 0.036 0.013 0.062 0.049 Number patents granted
0.057 0.028 0.112 0.036 0.178 0.132
Any patent commercialized
0.012 0.006 0.021 0.008 0.037 0.030
Number patents commercialized
0.029 0.017 0.054 0.019 0.084 0.074
Share immigrant 0.136 0.161 0.240 Observations 20,294 71,186 11,729 30,410 6724 15,502 Notes: Shares weighted with survey weights. Patents questions only asked of respondents who had ever worked. Whether a patent has been granted refers to period from October 1998 to the survey in 2003, and whether a patent has been commercialized or licensed refers to those patents granted in the same period. Source: 2003 National Survey of College Graduates.
Table 2: Means of aggregate variables (1) (2) (3) 1940-2000 1940 2000 Patents/population, x100 0.023
(0.015) 0.018
(0.013) 0.035
(0.020) Share of population 18-65 that is: Immigrant, college education and above 0.015 0.003 0.035 Native, college education and above 0.127 0.041 0.200 Immigrant, post-college education 0.007 0.001 0.016 Native, post-college education 0.050 0.011 0.077 Share of workers 18-65 that are: Immigrant, scientists and engineers 0.003 0.001 0.009 Native, scientists and engineers 0.022 0.006 0.035 Age of population 18-65 38.7
(1.0) 37.7 (1.0)
39.5 (0.6)
DoD prime military procurement contracts (millions of nominal $)
3236 (4386)
1500 (1679)
5528 (5809)
State personal income per capita (nominal $) 11976 (11098)
594 (204)
29,851 (4094)
Land area (millions of square kilometers) 0.190 (0.161)
0.166 (0.145)
0.207 (0.173)
Observations 343 49 49 Notes: Means of state-level variables for population 18-65, weighted by state population the year after the census. Standard deviations in parentheses. Patents and population are led by one year. Alaska and Hawaii are excluded. Patents are classified by year filed. The predicted increases in immigrant college share (instruments) are based on states’ shares of 1940 immigrant high school graduates from various countries and national growth in college graduates from those countries (see text). The 1940 value of DoD procurement spending is not available, and the 1950 value is given instead of 1940, and the 1950-2000 average instead of 1940-2000. Sources: Education, age, occupation, nativity: U.S. Census Bureau, IPUMS decennial census microdata usa.ipums.org/usa/ Patents: U.S. Patent and Trademark Office, electronic and paper data. State income, population: Bureau of Economic Analysis www.bea.gov/regional/spi/ Land Area: U.S. Census Bureau www.census.gov/population/censusdata/90den_stco.txt
Table 3: Patenting by field of study and field of study by immigrant status, college graduates (1) (2) (3) (4) Field of highest degree
Any patent granted
Any patent commercialized
Share immigrants
Share natives
Computer science, math 0.017 0.012 0.079 0.036 Biological, agricultural and environment sciences
0.023 0.011 0.055 0.040
Physical sciences 0.066 0.039 0.036 0.017 Social and related sciences 0.004 0.002 0.093 0.108 Engineering 0.061 0.042 0.137 0.053 Other S&E (mainly health) 0.007 0.004 0.166 0.121 Non-S&E 0.004 0.003 0.434 0.624 All fields 0.011 0.007 1.00 1.00 Notes: Shares weighted by survey weights. “S&E” means science and engineering. Full sample (i.e. college graduates), 91,480 observations. Whether a patent has been granted refers to period from October 1998 to the survey in 2003, and whether a patent has been commercialized or licensed refers to those patents granted in the same period. Source: 2003 National Survey of College Graduates.
Table 4: Effect of immigrant status on patenting (1) (2) (3) (4) (5) (6) Any patent granted? Any patent
commercialized? College graduates 0.0100**
(0.0010) 0.0009** (0.0005)
-0.0007* (0.0004)
-0.0005 (0.0003)
0.0062** (0.0008)
-0.0004 (0.0003)
Pseudo-R2 0.01 0.15 0.19 0.21 0.01 0.18 Post-college graduates
0.0226** (0.0018)
0.0014** (0.0008)
0.0004 (0.0006)
0.0005 (0.0006)
0.0135** (0.0014)
0.0002 (0.0004)
Pseudo-R2 0.02 0.21 0.24 0.26 0.02 0.21 Scientists and engineers
0.0131** (0.0039)
0.0031 (0.0031)
-0.0095** (0.0027)
-0.0074** (0.0026)
0.0063** (0.0030)
-0.0052** (0.0020)
Pseudo-R2 0.00 0.08 0.12 0.13 0.00 0.09 Major field of highest degree
-- Y Y Y -- Y
Highest degree -- -- Y Y -- Y Age, age2, sex, employed
-- -- -- Y -- --
Notes: Marginal effect on dummy for foreign-born from weighted probits. There are 91,480 observations in the college graduate sample, 42,139 in the post-college sample and 22,226 in the scientist and engineer sample. All scientists and engineers are employed in the reference week. Post-college degrees include master’s (including MBA), PhD and professional. There are 30 major field of study dummies (we combine the two S&E teacher training categories into one). Standard errors are in parentheses. ** indicates coefficients significant at the 5% level, * indicates coefficients significant at the 10% level.
Table 5: Effect of share of immigrant college graduates on log patents per capita (1) (2) (3) (4)
Difference: 10 year 10 year 30 year 50 year Δ Immigrant college as share of population
14.7** (5.3)
13.2** (4.3)
12.1** (3.2)
14.9** (4.3)
Δ Native college as share of population
4.1** (1.9)
1.9 (2.3)
4.8** (1.8)
5.8** (2.1)
Δ Age (average) 0.064** (0.028)
0.104** (0.035)
0.163** (0.041)
0.137** (0.066)
Δ DoD procurement (log) -0.033 (0.025)
-0.039** (0.017)
-0.081** (0.035)
-0.063 (0.041)
Land area (log) 0.046** (0.007)
0.063** (0.013)
0.169** (0.032)
0.281** (0.055)
Population 1940 (log) -0.056** (0.015)
-0.062** (0.015)
-0.161** (0.032)
-0.252** (0.060)
State personal income per capita 1940 (log)
-0.223** (0.037)
-0.162** (0.048)
-0.544** (0.103)
-1.006** (0.189)
Weighted No Yes Yes Yes R2 0.47 0.64 0.63 0.70 Observations 294 294 196 98 Notes: The dependent variable is the difference in log patents per capita across periods ranging from ten to 50 years, with a lead of one year compared to the independent variables. Weighted least squares regressions have weights 1/(1/popt+1+1/popt-k+1), where k the length of the difference. Regressions also include year dummies. Standard errors clustered by state are in parentheses. ** indicates coefficients significant at the 5% level, * indicates coefficients significant at the 10% level.
Table 6: Effect of skilled immigrant shares on patents per capita (1) (2) (3) (4) Δ Log patents per capita Δ Patents per capita
Difference: 10 year 50 year 10 year 50 year Panel A. Skilled: college graduates as share of population Δ Skilled immigrant 13.2**
(4.3) 14.9** (4.3)
0.368** (0.173)
0.271* (0.158)
Δ Skilled native 1.9 (2.3)
5.8** (2.1)
-0.010 (0.108)
0.134* (0.081)
R2 0.64 0.70 0.49 0.42 Panel B. Skilled: post-college educated as share of population Δ Skilled immigrant 20.7*
(10.7) 29.8** (10.9)
0.686 (0.501)
0.538 (0.403)
Δ Skilled native -1.3 (3.3)
8.4 (5.8)
-0.086 (0.138)
0.127 (0.224)
R2 0.63 0.66 0.48 0.38 Panel C. Skilled: scientists and engineers as share of workers Δ Skilled immigrant 52.4**
(20.7) 52.6** (16.1)
2.318** (0.990)
1.354** (0.661)
Δ Skilled native 9.4* (5.4)
24.7** (8.0)
0.212 (0.239)
0.665** (0.278)
R2 0.67 0.74 0.56 0.52 Observations 294 98 294 98 Notes: The dependent variable is the difference in (log) patents per capita across periods ranging from ten to 50 years, with a lead of one year compared to the independent variables. Weighted least squares with weights 1/(1/popt+1+1/popt-k+1), where k is equal to the difference length. All regressions include the covariates of Table 5. Standard errors clustered by state are in parentheses. Coefficients in columns 3-4 are multiplied by 100. ** indicates coefficients significant at the 5% level, * indicates coefficients significant at the 10% level.
Table 7: Effect of college immigrant shares on log patents per capita, ten-year differences, further specifications
(1) (2) WLS IV 1. Base specifications
13.2** (4.3)
30.3** (7.2) [27]
2. Base specifications without California (288 observations) 9.2** (4.3)
26.3** (7.1) [24]
3. Base specifications without year 2000 (245 observations) 8.8** (3.5)
18.9** (7.1) [51]
4. Include BEA region dummies
11.5** (4.5)
23.4** (5.4) [30]
5. Include state dummies 11.6** (5.6)
24.5** (6.3) [31]
6. Include BEA region dummies and % electrical workers 1980*year dummies
9.6** (4.7)
23.1** (7.0) [28]
7. Include BEA region dummies and % electrical workers1980*year dummies and 1940 immigrant shares (λ)
10.1* (5.8)
24.5** (7.8) [39]
8. Include BEA region dummies and % electrical workers1980*year dummies; exclude share college natives
8.6* (4.3)
17.6** (5.6) [27]
9. Include BEA region dummies*post-1980 8.4** (3.4)
18.6** (7.6) [9]
10. Include BEA region dummies*post-1980; exclude share college natives
7.0** (3.4)
12.3** (6.1) [10]
Notes: Each coefficient reported is the effect of a change in college immigrant share of the population from a different regression. The dependent variable is the difference in log patents across ten years, with a lead of one year compared to the independent variables. 294 observations unless otherwise noted. Weighted least squares (column 1) or instrumental variables (column 2) with weights 1/(1/popt+1+1/popt). The instruments are the predicted increase in college immigrant shares, based on states’ shares of 1940 immigrants from various countries and subsequent national growth in college graduates from those countries (see text). F-statistic for test of joint significance of excluded instrument in the first stage in brackets. All regressions also include the covariates of Table 5 including the appropriate differenced share of skilled natives. Standard errors clustered by state are in parentheses. ** indicates coefficients significant at the 5% level, * indicates coefficients significant at the 10% level.
Table 8: Effect of skilled immigrant shares on log patents per capita, ten-year differences, preferred specifications
(1) (2) (3) (4) (5)
Skill represented by: College graduates Post-college Scientists/ engineers
WLS IV WLS IV WLS 1. Include BEA region dummies, % electrical workers1980*year dummies; IV excludes share college natives
9.6** (4.7)
17.6** (5.6) [27]
11.3 (8.3)
18.9 (14.3) [18]
38.2* (20.3)
2. Include BEA region dummies*post-1980; IV excludes share college natives
8.4** (3.4)
12.3** (6.1) [10]
15.9** (6.2)
27.0** (13.4) [11]
30.7* (16.3)
Notes: Each coefficient reported is the effect of a change in skilled immigrant share from a different regression. The dependent variable is the difference in log patents across ten years, with a lead of one year compared to the independent variables. Weighted least squares (odd columns) or instrumental variables (even columns) with weights 1/(1/popt+1+1/popt). The instruments are the predicted increase in skilled immigrant shares, based on states’ shares of 1940 immigrants from various countries and subsequent national growth in college graduates from those countries (see text). F-statistic for test of joint significance of excluded instrument in the first stage in brackets. All regressions also include the covariates of Table 5 including the appropriate differenced share of skilled natives. Standard errors clustered by state are in parentheses. 294 observations. ** indicates coefficients significant at the 5% level, * indicates coefficients significant at the 10% level.
Table 9: Effect of skilled immigrant shares on log patent citations per capita and log patents per capita by type, ten-year differences, 1970-2000
(1) (2) (3)
Skill represented by: College graduates Post-college Scientists/engineers 1. Patents 10.7**
(4.6) 15.2
(11.6) 45.7** (22.0)
2. Patent citations
9.9** (4.8)
18.5 (12.4)
54.4** (24.2)
3. Patent citations, include BEA region dummies
11.3** (5.6)
24.2* (12.2)
56.2* (29.6)
4. Computer and communications patents (137 observations)
10.2 (7.4)
1.7 (19.5)
35.0 (23.5)
5. Electrical and electronic patents (145 observations)
0.1 (6.1)
-2.2 (15.4)
6.9 (23.9)
6. Drug and medical patents (146 observations)
12.5* (6.7)
9.2 (14.8)
50.6 (30.7)
7. Chemical patents (145 observations)
7.5 (6.4)
8.7 (14.9)
10.3 (26.5)
8. Mechanical patents -3.0 (3.9)
-15.7 (9.0)
3.8 (16.1)
9. Other patents -7.7** (2.6)
-19.2** (4.9)
-15.5 (9.7)
Notes: Each coefficient reported is the effect of a ten-year change in skilled immigrant share from a different regression. The dependent variable is the difference in log patents per capita or log of patent citations per capita across ten years, with a lead of one year compared to the independent variables. Weighted least squares for 1970-2000 with weights 1/(1/popt+1+1/popt). All regressions include the covariates included in Table 5. Standard errors clustered by state are in parentheses. 147 observations, unless otherwise specified. ** indicates coefficients significant at the 5% level, * indicates coefficients significant at the 10% level.
Appendix Table 1: States’ 1940 shares of national-level immigrants from various origins (1) (2) (3) (4) State’s 1940 share of national total, all immigrants College grad immigrants Origin Mean Maximum State of maximum National total 2000 -
national total 1940 United Kingdom 0.050 0.19 New York 192,750 Ireland 0.059 0.32 New York 22,667 Italy 0.062 0.35 New York 45,368 Germany 0.052 0.23 New York 216,513 Poland 0.060 0.28 New York 66,284 Russia 0.064 0.37 New York 236,052 Other Europe 0.050 0.19 New York 348,471 Canada 0.038 0.21 Massachusetts 208,124 Mexico 0.043 0.39 California 263,006 Puerto Rico 0.096 0.90 New York 121,761 Cuba 0.047 0.41 Florida 125,089 Other Caribbean 0.073 0.61 New York 234,065 Central America 0.052 0.26 California 130,725 South America 0.069 0.47 New York 368,186 China 0.058 0.39 California 617,482 India 0.047 0.26 California 773,840 Other Asia 0.045 0.62 California 1,426,943 Rest of world 0.054 0.26 New York 549,302 Notes: State-level variables, means weighted by state population. Standard deviations in parentheses. 49 observations. Alaska and Hawaii are excluded. The minimum share is zero for all origins except for the United Kingdom, Germany, other Europe and Canada. Columns 1-3 are based on the full population, while column 4 is based on the population 18-65.
Appendix Table 2: Means of individual-level variables College graduates Post-college Scientists/engineers Immigrant Native Immigrant Native Immigrant Native Highest degree: Bachelor’s 0.58 0.65 -- -- 0.44 0.68 Master’s 0.28 0.26 0.66 0.74 0.39 0.26 Doctorate 0.07 0.03 0.17 0.08 0.16 0.06 Professional 0.07 0.06 0.17 0.17 0.01 0.01 Field of highest degree Computer science, mathematics
0.076 0.036 0.091 0.027 0.219 0.168
Biological, agricultural, environment science
0.056 0.040 0.061 0.030 0.092 0.093
Physical science 0.035 0.017 0.044 0.017 0.077 0.072 Social science 0.091 0.108 0.069 0.078 0.026 0.046 Engineering 0.132 0.053 0.131 0.037 0.397 0.321 Other S&E 0.164 0.121 0.199 0.157 0.069 0.058 Non-S&E 0.446 0.624 0.406 0.653 0.120 0.243 Sex (female) 0.48 0.50 0.43 0.49 0.24 0.23 Age 43.4
(9.9) 44.7
(10.3) 43.8 (9.9)
46.6 (10.3)
40.4 (9.0)
42.4 (9.5)
Employed 0.86 0.85 0.89 0.87 1.00 1.00 Observations 21,248 71,304 12,042 30,460 6840 15,519 Notes: Means weighted with survey weights. S&E means science and engineering. “Other S&E” includes the social sciences. Native movers are natives living in a different census region from their census region of birth. Source: National Survey of College Graduates
Appendix Table 3: First stage of instrumental variables regressions for ten-year differences
(1) (2) Skill represented by: College graduates Post-college
1. Base specifications
0.31** (0.06)
0.29** (0.06)
R2 [R2 without excluded instrument] 0.78 [0.69] 0.75 [0.67] 2. Sample without California (288 observations)
0.25** (0.05)
0.24** (0.06)
R2 [R2 without excluded instrument] 0.70 [0.63] 0.69 [0.63] 3. Sample without year 2000 (245 observations)
0.45** (0.06)
0.40** (0.06)
R2 [R2 without excluded instrument] 0.79 [0.59] 0.69 [0.55] 4. Include BEA region dummies 0.29**
(0.05) 0.27** (0.06)
R2 [R2 without excluded instrument] 0.83 [0.76] 0.80 [0.74] 5. Include state dummies 0.34**
(0.06) 0.33** (0.07)
R2 [R2 without excluded instrument] 0.89 [0.82] 0.86 [0.79] 6. Include BEA region dummies and % electrical workers 1980*year dummies
0.25** (0.05)
0.25** (0.06)
R2 [R2 without excluded instrument] 0.83 [0.79] 0.80 [0.76] 7. Include BEA region dummies and % electrical workers 1980*year dummies and 1940 immigrant shares
0.29** (0.05)
0.30** (0.06)
R2 [R2 without excluded instrument] 0.89 [0.85] 0.85 [0.81] 8. Include BEA region dummies and % electrical workers 1980*year dummies; exclude native skilled share
0.27** (0.05)
0.29** (0.06)
R2 [R2 without excluded instrument] 0.83 [0.78] 0.84 [0.80] 9. Include BEA region dummies*post-1980 0.25**
(0.09) 0.26** (0.08)
R2 [R2 without excluded instrument] 0.81 [0.77] 0.78 [0.73] 10. Include BEA region dummies*post-1980; exclude native skilled share
0.27** (0.09)
0.26** (0.08)
R2 [R2 without excluded instrument] 0.81 [0.76] 0.77 [0.73] Notes: The dependent variable is the ten-year difference in the share of the population that is a skilled immigrant, with skill proxied by college in column 1, post-college in column 2. The coefficient reported is that on the excluded instrument, which is the predicted increase in immigrant college shares, based on states’ shares of 1940 immigrant graduates from various countries and subsequent national growth in college graduates from those countries (see text). Weighted least squares with weights 1/(1/popt+1+1/popt). All regressions also include the covariates of Table 5 (except the difference in the skilled immigrant share). Standard errors clustered by state are in parentheses. 294 observations unless otherwise specified. ** indicates coefficients significant at the 5% level, * indicates coefficients significant at the 10% level.
Patents
Patents per 100,000
0
10
20
30
40
50
60
70
8085
Pate
nts
per 1
00,0
00 re
siden
ts
0
20000
40000
60000
80000
100000Nu
mbe
r of p
aten
ts
1941 1951 1961 1971 1981 1991 2001Year (Application Date)
Source: USPTO, BEA and authors’ calculations
Figure 1: U.S. Origin U.S. Patents 1941−2001
Patents, all states
Patents, without California
Patents per capita
.5
.75
1
1.25
1.5
1.75St
anda
rd d
evia
tion
of lo
g pa
tent
s
1930 1940 1950 1960 1970 1980 1990 2000Year (Application Date)
Source: USPTO, BEA and author’s calculations
Figure 2: Convergence in Patenting Across States 1929−2001
AL
AZ
AR CA
COCT
DEDC
FLGA
ID
IL
IN IAKSKY
LA
ME
MDMAMI
MNMS
MOMTNENV
NHNJNM
NYNC
ND
OHOK OR
PA
RI
SCSDTN
TXUT
VT
VA
WA
WVWI
WY
−.005
0
.005
.01
0 .001 .002 .003 .004
1940−50: slope 0.24 (0.19)
AL
AZ
AR CACO
CT
DE
DC
FLGA
ID
ILINIAKS
KY
LA
ME
MDMAMI
MN
MSMOMT
NENV
NH
NJNMNYNCND
OHOKOR
PA
RI
SCSDTNTXUT
VT
VA WAWV
WIWY
−.01
−.005
0
.005
−.0015 −.0005 0 .0005 .0015
1950−60: slope 0.22 (0.42)
AL AZAR
CA
COCT
DE
DC
FL
GA ID
IL
IN
IAKSKY LA ME
MD
MAMIMN
MSMO
MTNE
NV NHNJ
NM
NY
NC ND
OHOK
ORPA
RI
SCSD
TNTX UT
VTVA
WAWVWI
WY0
.002
.004
.006
.008
0 .002 .004 .006 .008 .01
1960−70: slope 0.37 (0.05)
ALAZ
AR
CA
CO
CT
DE
DC
FL
GA
ID
IL
INIA
KSKY
LAME
MD
MA
MIMNMSMOMTNE
NVNH
NJ
NM
NY
NC NDOHOK ORPA
RISC
SDTN
TX
UTVTVA
WA
WVWI WY
−.005
0
.005
.01
.015
0 .01 .02 .03
1970−80: slope 0.50 (0.05)
AL
AZ
AR
CA
CO
CT
DE
DC
FL
GA
ID
IL
INIAKSKY
LAME
MD MA
MIMNMSMO MTNE
NVNH
NJ
NM
NY
NC
NDOHOK
ORPA
RI
SCSD
TN
TX
UTVT
VA
WA
WVWI WY0
.005
.01
.015
.02
0 .01 .02 .03 .04
1980−90: slope 0.46 (0.05)
AL
AZ
AR
CA
COCT
DE
DC
FL
GA
ID
IL
IN IAKSKY LAME
MDMA
MIMN
MS
MOMT
NE
NV
NH
NJ
NM
NY
NC
NDOHOK
OR PARI
SCSD
TN
TX
UTVT
VA WA
WVWI
WY0
.01
.02
.03
0 .02 .04 .06
1990−2000: slope 0.33 (0.05)
Actu
al c
hang
e in
imm
igra
nt c
olle
ge s
hare
Predicted change in immigrant college share of population (instrument)
Fig 3: Actual, Predicted Change in Immigrant College Share
